Cable dome is one of tension structure which is gradually stabilized by tensioning tables from initially unstable state to finally stable state. This stabilizing process is not able to be developed by general analysis because some cables endure compression forces during stabilizing process. Thus, this paper uses dynamic relaxation method to solve this problem. To apply this stabilizing process analysis to the actual project, this paper deals with cable dome roof of Seoul Olympic Gymnasium. Finally, this paper prove the usefulness of stabilizing process analysis by comparing the analysis results and the measurements.